Relativistic Mean Field Modelwith the TMA parameterfor unstable nuclei
Hiroshi Toki (RCNP/Osaka)
Lisheng Geng (RCNP: Beijing/China)
06.4.10

Jan 13, 2006 RIKEN

Supernova explosion

February 23, 1987

Before06.4.10After
Jan 13, 2006 RIKEN

Supernova explosion and neutrino propagation

Fe coreCollapseνρc ~1010 g/cm3
Tc ~1 MeV

e-captureν-trappingρc ~1012 g/cm3
Tc ~2 MeVνν ν

1000 kmννCore BounceExplosion

ρc ~3x1014 g/cm3
Tc ~5 MeV

NS R-processνν ν
06.4.10

ν

Shockwave

Jan 13, 2006 RIKEN10 km

Bethe-Weizsaecker Ｍ ａ ｓ ｓ Fｏ ｒ
ｍ ｕ ｌ ａLiquid drop model

06.4.10

Jan 13, 2006 RIKENhMass as compared with simple
BW mass formula06.4.10

Jan 13, 2006 RIKEN

Nuclear matter saturation
non-relativistic

relativistic Bruckner Hartree-FockCoester band

Empirical saturation

relativistic mean field theory

 Non-relativistic calculations: notsuccessful.
 Relativistic Bruckner Hartree-Fockcalculations: encouraging!
 The RMF model: parameterized todescribe the nuclear matter saturation.
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Jan 13, 2006 RIKEN

Relativistic mean field theory withTMA parameter
Y. Sugahara and H. Toki

LagrangianNucl. Phys. A579 (1994) 557

7 free parameters
TMA
06.4.10

Jan 13, 2006 RIKENThe relativistic mean field (RMF) model

Dirac equation

Klein-Gordon equation

Scalar and Vector potentials

06.4.10

Jan 13, 2006 RIKENThe RMF model

Y. Sugahara and H. Toki, Nucl. Phys. A 579 (1994)557
06.4.10

Jan 13, 2006 RIKENThe effective force TMA:
Parameter values of TMA

Saturation properties of SNM

To describe simultaneously both light and heavy nuclei
06.4.1013, 2006 RIKEN
To
simulate the nuclearJansurface
effectThe pairing correlation in weakly bound nuclei
 The constant-gap BCS method: very successful forstable nuclei

 But for weakly bound nuclei, which are the subjects ofpresent research, it fails.
 A zero-range delta force in the particle-particle channel isfound to be useful!

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Jan 13, 2006 RIKEN

Study all nuclei within RMF
 Calculate all 7000 Nuclei
 Deformation and pairing are workedout
 Many predictions for experiments tocome

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Proton separation Energy

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Proton radius for neutron magic number nuclei

06.4.10

Jan 13, 2006 RIKEN

Quadrupole-constrained calculation and the true ground-state

Z=58

Z=71

Z=6406.4.10

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The potential energy surfaces of 14 N=116 isotones

Binding Energy

06.4.10

Z=64

Z=66

Z=68

Z=70

Jan 13, 2006 RIKEN

Deformation

06.4.10

Z=64

Z=66

Z=68

Z=70

Jan 13, 2006 RIKEN

Radius

Z=64

Z=66

Z=6806.4.10

Z=70

Jan 13, 2006 RIKEN

Proton drip line: theory vs. experiment

N=Z

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Proton separation energy [MeV]Proton emission beyond the proton drip line

06.4.10

proton emitter
E=1.7

E=0.8

E=0.0

Jan 13, 2006 RIKEN

Studies of the rare-earth proton emission in RMF+BCS model

06.4.10

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Proton skin in Ar isotopes

A. Ozawa et al., NPA709(2002)606.4.10

Jan 13, 2006 RIKEN

Separation Energy

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Nuclear Radius

06.4.10

Jan 13, 2006 RIKENSingle particle Energy and Fermi Energy

06.4.10

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Binding energy difference

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Nuclear deformation
Exp

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Jan 13, 2006 RIKEN

Summary of RMF for Finite Nuclei
 The RMF lagrangian is very good forfinite nuclei.
 The isovector interaction is not wellcontrolled yet Rho meson tensor coupling Pion exchange term

06.4.10

Jan 13, 2006 RIKEN